"Madiba is stable and we are thankful that he is responding well to treatment and that he is much better," Zuma said on Thursday.
Mandela has spent just over a week in hospital, where he is being treated for pneumonia.
"We remain thankful for all the support to the family during this difficult time," Zuma said.
Zuma also met members of the family, who expressed their gratitude for the support from South Africans and people all over the world, his spokesperson Mac Maharaj said.
This is the third health scare in four months for the Nobel Peace Prize laureate, who became South Africa's first black president in 1994 and was hailed as a global symbol of tolerance and harmony.
He was in hospital briefly in early March for a check-up and was hospitalised in December for nearly three weeks with a lung infection and after surgery to remove gallstones.
Mandela stepped down as president in 1999 and has not been politically active for a decade. But he is still revered at home and abroad for leading the struggle against apartheid rule and then championing racial reconciliation while in office.
Mandela has a history of lung problems dating back to when he contracted tuberculosis as a political prisoner. He spent 27 years in prison on Robben Island and in other jails for his attempts to overthrow the white-minority government. – Reuters, Sapa